Elliptic curve isogeny class with Cremona label 227850gj (LMFDB label 227850.dr)

• Label: 227850gj
• Number of curves: $4$
• Conductor: $227850$
• CM: no
• Rank: $1$

Elliptic curves in class 227850gj

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
227850.dr4	227850gj1	\([1, 0, 1, 1701499, 958601648]\)	\(296354077829711/387386634240\)	\(-712119533307840000000\)	\([2]\)	\(12441600\)	\(2.6871\)	\(\Gamma_0(N)\)-optimal
227850.dr3	227850gj2	\([1, 0, 1, -10450501, 9343481648]\)	\(68663623745397169/19216056254400\)	\(35324215660529775000000\)	\([2]\)	\(24883200\)	\(3.0337\)
227850.dr2	227850gj3	\([1, 0, 1, -48572501, 131073005648]\)	\(-6894246873502147249/47925198774000\)	\(-88099245477536343750000\)	\([2]\)	\(37324800\)	\(3.2364\)
227850.dr1	227850gj4	\([1, 0, 1, -778452001, 8359734488648]\)	\(28379906689597370652529/1357352437500\)	\(2495174326866210937500\)	\([2]\)	\(74649600\)	\(3.5830\)

Rank

The elliptic curves in class 227850gj have rank \(1\).

Complex multiplication

The elliptic curves in class 227850gj do not have complex multiplication.

Modular form 227850.2.a.gj

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.